Subgroups — C₃×D₃×C₁₇⋊D₁₇ #23780914

Order 10404.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₁₇⋊D₁₇	—	3	1	no	maximal
5	D₃×C₁₇⋊D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₇²	—	3	1	no	—
8	C₃×C₁₇⋊D₁₇	—	2	1	no	—
9	C₃×C₁₇⋊D₁₇	—	3	1	no	—
10	C₃×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic, direct product factor
11	C₃×C₁₇⋊D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
12	D₃×C₁₇²	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₁₇⋊D₁₇	—	3	1	no	Hall
15	C₃×C₁₇²	—	2	1	no	—
16	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₁₇	—	17	18	no	maximal
19	C₂×C₁₇²	—	3	1	no	—
20	C₁₇⋊D₁₇	—	3	1	no	—
21	C₁₇⋊D₁₇	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₃×D₅₁	—	17	18	no	—
23	C₃×D₃×C₁₇	D₁₇	1	18	yes	complemented
24	C₃²×D₁₇	—	17	18	no	—
25	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×D₁₇	—	51	18	no	—
27	D₃×D₁₇	—	17	18	no	—
28	C₃²×C₁₇	C₂×D₁₇	1	18	yes	complemented
29	C₂×C₃×C₁₇	—	3	18	no	—
30	D₅₁	—	17	18	no	—
31	C₃×D₁₇	—	17	18	no	—
32	C₃×D₁₇	—	17	18	no	—
33	C₃×D₁₇	—	34	18	no	—
34	C₃×D₁₇	—	51	18	no	—
35	D₃×C₁₇	C₃×D₁₇	1	18	yes	complemented
36	C₂×D₁₇	—	51	18	no	—
37	C₃×C₁₇	—	2	18	no	—
38	C₃×C₁₇	D₃×D₁₇	1	18	yes	complemented
39	C₃×C₁₇	C₂×C₃×D₁₇	1	18	yes	complemented
40	C₂×C₃×D₃	—	289	1	no	Hall
41	C₂×C₁₇	—	3	18	no	—
42	D₁₇	—	17	18	no	—
43	D₁₇	—	51	18	no	—
44	C₂×C₃²	—	289	1	no	—
45	C₃×D₃	—	289	1	no	—
46	C₃×D₃	C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor
47	C₁₇	C₃×D₃×D₁₇	1	18	yes	complemented
48	C₂²×C₃	—	867	1	no	—
49	C₂×D₃	—	289	1	no	—
50	C₃²	C₂×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	3	1	no	—
52	C₂×C₃	—	289	1	no	—
53	C₂×C₃	—	289	1	no	—
54	C₂×C₃	—	578	1	no	—
55	C₂×C₃	—	867	1	no	—
56	D₃	—	289	1	no	—
57	D₃	C₃×C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor
58	C₂²	—	867	1	no	Sylow
59	C₃	—	2	1	no	—
60	C₃	D₃×C₁₇⋊D₁₇	1	1	yes	characteristic, direct product factor
61	C₃	C₂×C₃×C₁₇⋊D₁₇	1	1	yes	characteristic, complemented
62	C₂	—	3	1	no	—
63	C₂	—	289	1	no	—
64	C₂	—	867	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×C₁₇⋊D₁₇
commutator, cosocle, hypocenter	C₃×C₁₇²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₂²
LCS	G ▷ C₃×C₁₇²
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	semidirect
2. C₃×D₃×C₁₇²	C₂	semidirect
3. C₃²×C₁₇⋊D₁₇	C₂	semidirect
5. D₃×C₁₇⋊D₁₇	C₃	direct (N × H)
6. C₃²×C₁₇²	C₂²	semidirect
10. C₃×C₁₇⋊D₁₇	D₃	direct (N × H)
11. C₃×C₁₇⋊D₁₇	C₂×C₃	semidirect
12. D₃×C₁₇²	C₂×C₃	semidirect
13. C₃⋊(C₁₇⋊D₁₇)	C₂×C₃	semidirect
16. C₃×C₁₇²	C₂×D₃	semidirect
17. C₃×C₁₇²	C₂²×C₃	semidirect
21. C₁₇⋊D₁₇	C₃×D₃	direct (N × H)
23. C₃×D₃×C₁₇	D₁₇	semidirect
25. C₁₇²	C₂×C₃×D₃	semidirect
28. C₃²×C₁₇	C₂×D₁₇	semidirect
35. D₃×C₁₇	C₃×D₁₇	semidirect
38. C₃×C₁₇	D₃×D₁₇	semidirect
39. C₃×C₁₇	C₂×C₃×D₁₇	semidirect
46. C₃×D₃	C₁₇⋊D₁₇	direct (N × H)
47. C₁₇	C₃×D₃×D₁₇	semidirect
50. C₃²	C₂×C₁₇⋊D₁₇	semidirect
57. D₃	C₃×C₁₇⋊D₁₇	direct (N × H)
60. C₃	D₃×C₁₇⋊D₁₇	direct (N × H)
61. C₃	C₂×C₃×C₁₇⋊D₁₇	semidirect

Subgroups — C3×D3×C17⋊D17 #23780914

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×C₁₇⋊D₁₇ #23780914